Which of the following numbers is a factor of 164? ${3,4,5,7,12}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $164$ by each of our answer choices. $164 \div 3 = 54\text{ R }2$ $164 \div 4 = 41$ $164 \div 5 = 32\text{ R }4$ $164 \div 7 = 23\text{ R }3$ $164 \div 12 = 13\text{ R }8$ The only answer choice that divides into $164$ with no remainder is $4$ $ 41$ $4$ $164$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $4$ are contained within the prime factors of $164$ $164 = 2\times2\times41 4 = 2\times2$ Therefore the only factor of $164$ out of our choices is $4$. We can say that $164$ is divisible by $4$.